Modeling the effects of aluminum and ammonium perchlorate addition on thedetonation of the high explosives C4H8O8N8 (HMX) and C3H6O6N6 (RDX)Donghyeon Baek, Bohoon Kim, and Jack J. Yoh

Citation: Journal of Applied Physics 124, 215905 (2018); doi: 10.1063/1.5058155View online: https://doi.org/10.1063/1.5058155View Table of Contents: http://aip.scitation.org/toc/jap/124/21Published by the American Institute of Physics

Modeling the effects of aluminum and ammonium perchlorate addition on thedetonation of the high explosives C4H8O8N8 (HMX) and C3H6O6N6 (RDX)

Donghyeon Baek,1 Bohoon Kim,2 and Jack J. Yoh1,a)1Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742,South Korea2Graduate Aeronautical Laboratory, California Institute of Technology, Pasadena, California 91125, USA

(Received 17 September 2018; accepted 15 November 2018; published online 4 December 2018)

Metalized high explosives effectively tailor the explosion impulse at lowered detonation pressures ofcommon high performance explosives such as C3H6O6N6 (RDX) and C4H8O8N8 (HMX). The pres-ence of aluminum (Al) with and without ammonium perchlorate (AP) allows the subsequentburning for longer and sustained reactions of enhanced blast explosives. The modeling of reactionrate laws for three explosives with varied amounts of Al, AP, RDX, and HMX is reported. Themodel validation included the rate stick test for understanding the explosive reaction of the threesamples and the large-scale gap test for determining their ignition sensitivity. The experimentalresults confirmed the accuracy of the model in simulating the shock sensitivity and the size effectsbefore detonation failure. The effect of enhanced blast of these explosives in the presence of Al andAP is also reported. Published by AIP Publishing. https://doi.org/10.1063/1.5058155

I. INTRODUCTION

The addition of fine metallic powders to high perfor-mance explosives such as RDX and HMX can effectivelyextend the reaction duration, often tailored to meet certainperformance needs. Al particles can react with hot explosiveproduct gases from the detonation of either RDX or HMX,further burning in air, or with additional oxidizers such asammonium perchlorate (AP) to increase the energy releaseduring the whole reaction process. Furthermore, hot metalparticles may be ejected from the fireballs of these metalizedenhanced blast explosives. The fuel-rich condition due to thepresence of Al may lower the peak pressure of detonationwhile enhancing the impulse for a longer subsequentburning. However, the effect of AP on providing additionaloxygen for Al in hot product gases is still under investigationby many researchers.

Xiang et al.1 analyzed the detonation characteristics ofHMX–Al explosives in underwater environments; by increas-ing the Al content, the peak detonation pressure decreased,while the impulse initially increased and then decreased, sug-gesting the existence of an optimal Al concentration for max-imizing the impulse. Increasing the Al content also increasedthe bubble energy due to the subsequent Al reaction. In thesubsequent study,2 the combustion characteristics of anRDX–Al–AP mixture were considered. The bubble energydue to the subsequent reaction was greater than that of RDX–Al in the absence of AP, since AP promotes Al burning, andcontributed to enhancing the underwater chemical explosionfollowing the hydrodynamic bubble collapse. Kim et al.3

used a two-phase model to reproduce the detonation charac-teristics of HMX–Al explosives with increasing Al contents.As the Al content increased, the detonation velocity clearlydeclined, and the double peak due to the subsequent reaction

of Al was observed in the numerical simulations. A modifiedreaction model4,5 was used to determine the rate parametersof 50% RDX and was verified by the unconfined rate stickand gap tests.

In this paper, a pressure-driven reaction model is devel-oped and verified for understanding the chemical reactioncharacteristics of enhanced blast explosives summarized inTable I, which are designed to isolate the effect of Al and APaddition on the detonation of the basic explosives includingAl, AP, and HTPB (hydroxyl terminated polybutadiene). Inparticular, we focus on the effects of a fuel-rich conditiondue to Al in excess and on how the oxygen-rich conditiondue to AP addition can boost the burning subsequent to thebasic explosive detonation. A series of unconfined rate stickand large-scale gap tests (LSGTs) are conducted to assess thevalidity of the results obtained from the empirically inspiredreaction rate law.

II. EXPERIMENTAL TESTS

A. Unconfined rate stick test

Detonation failure occurs when the chemical energygenerated is smaller than the lateral loss due to the productexpansion in the reaction zone. With increasing lateral loss,the detonation speed nears the sound speed, then the reactionstops or the detonation failure occurs.6

The unconfined rate stick test was performed to measurethe fully developed detonation velocities with respect to theexplosive radius before a detonation failure point. The testwas conducted with the explosive length which was tentimes the diameter to allow a fully developed detonationspeed.4 If the explosive detonates successfully, the detectorconnected to each electric pin records the time that the deto-nation wave takes to reach the pins, and the detonation speedcan be derived by a linear fit. In the case of failure, no signalis transmitted to the detector.a)jjyoh@snu.ac.kr

JOURNAL OF APPLIED PHYSICS 124, 215905 (2018)

0021-8979/2018/124(21)/215905/7/$30.00 124, 215905-1 Published by AIP Publishing.

Figure 1 shows the size effects for the three explosives ofTable I. RDX 25 has the most gradual trend with the largestcritical radius of detonation failure. This has the minimumconcentration of the main explosive, RDX, while containingboth Al and AP. The effect of lateral loss is greater when theexplosive radius is of the same order of the reaction zonelength.6 Hence, RDX 25 has the largest critical radius with atendency to decline gradually from a larger radius. On theother hand, the reaction of HMX 95, which does not containany metal, occurs within 1 μs. Therefore, when the radius isof the same order of the reaction zone length, the detonationvelocity declines rapidly, as shown in Fig. 1.

B. Large-scale gap test

The large-scale gap test measures the sensitivity of theacceptor explosive. The detonation pressure wave generatedby the impact at the donor is attenuated through the gap untilreaching the acceptor charge. As shown in Fig. 2, a cylindricalconfiguration is used with pentolite (length of 50mm anddiameter of 50.8 mm) as the donor and polymethyl methacry-late (PMMA) as the gap material. The PMMA thickness isincreased incrementally using additional layers (disc) until theacceptor failure is witnessed with a probability of 50%.5 Thecritical gap thickness for each explosive and the correspondingshock pressure are shown in Table II. The gap thicknessincreased with increasing the percentage of basic explosive.

III. REACTION RATE LAW

The reactive flow model follows Eq. (1). The first termis associated with the effect of compression by the shock

wave, which gives rise to a second (growth) term. λ is thereaction progress, p is the pressure, t is the time, ρ0 and ρ arethe initial and instantaneous densities, and μ ¼ ρ=ρ0 � 1

dλ

dt¼ I(1� λ)μaj0�λ�0:01 þ G(1� λ)pbj0:01,λ�1: (1)

This model originates from the Lee-Tarver ignition andgrowth (I&G) model7 and, at the same time, complementsthe difficulty associated with determining the model parame-ters. The ignition parameter (I) is determined by gap test sim-ulations where Go/No Go is known for the correspondinggap thickness. The growth parameters (G, b, a) are deter-mined with the method described in Ref. 4. Their values areverified by reproducing the size effect curve from unconfinedrate stick experiments. The reaction rate parameters used inour simulation are shown in Table III.

IV. GOVERNING EQUATION AND MODELINGCONSTANTS

We performed a multi-material numerical simulationfor shock to detonation transition (SDT) by using a housecode and applied a hybrid particle level-set method basedon the ghost fluid method (GFM) framework to handlethe interface between explosive and inert.8 The equationfor mass, momentum, and energy conservation in a two-dimensional axi-symmetry is

@U!@t

þ @ E!@r

þ @ F!@z

¼ S!(U!), (2)

U!¼

ρ

ρurρuzρE

26664

37775, E

!¼

ρur

ρu2r þ p

ρuruzur(ρEþ p)

26664

37775, F

!¼

ρuz

ρuzurρu2z þ p

uz(ρEþ p)

26664

37775,

(3)

FIG. 1. Rate stick data for three explosives.

FIG. 2. LSGT configuration determining the maximum PMMA gap thick-ness for acceptor ignition upon donor initiation.

TABLE I. Properties of the three explosives used.

Explosives Composition (%)

RDX 25 RDX 25, Al 35, AP 25, HTPB 15HMX 66 HMX 66, Al 25, HTPB 9HMX 95 HMX 95, HTPB 5

TABLE II. LSGT data for the three explosives.

AcceptorDensity(kg m−3)

Critical gap thickness(mm)

Shock pressure(GPa)

RDX 25 1830 21.45 6.248HMX 66 1900 43.79 2.859HMX 95 1820 53.49 1.827

215905-2 Baek, Kim, and Yoh J. Appl. Phys. 124, 215905 (2018)

where w is 0 for rectangular and 1 for cylindrical coordinates,and uz and ur are the axial and radial velocities, respectively.E ¼ eþ (u2z þ u2r )=2 is the total energy per unit mass, e isthe specific internal energy, p is the pressure, and η is 0 forfluids and 1 for the gap material. For the LSGT, the devia-toric stresses of the PMMA discs are also needed such that

_sij ¼ _sij,tr þ _sij,cor ¼ Ωikskj � sikΩkj þ 2G0��Dij � Dp

ij

�, (5)

_sij,tr ¼ Ωikskj � sikΩkj þ 2G0 �Dij , (6)

_sij,cor ¼ �H:Dpij ¼ �2G0ΛNij,tr, (7)

where G0 is the shear modulus, and each operator is definedas follows:

Dij ¼ Dij � 13Dkkδij, Dij ¼ 1

2@ui@xj

þ @uj@xi

� �,

Ωij ¼ 12

@ui@xj

� @uj@xi

� �:

(8)

For time discretization, the third order Runge–Kutta methodwas used, with the convex essentially non-oscillatory (ENO)scheme for the spatial fluxes.8 The rate of burned mass

production is defined as

@(ρλi)@t

þ @(ρλiuj)@xj

¼ wi, (9)

where wi is the reaction rate and λi is the reaction progressvariable. The pressure in the unreacted state for donor andacceptor explosives was calculated, respectively, in the poly-nomial form9 and by the Mie–Gruneisen equation of state(EOS)10

punreacted(donor) ¼ A1(ρ=ρ0 � 1)1 þ B1(ρ=ρ0 � 1)2

þ C1(ρ=ρ0 � 1)3, (10)

punreacted(acceptor) ¼ pH þ Γρ(e� eH), (11)

where pH and eH are the pressure and internal energy in thereference state according to the Hugoniot curve, respectively,Γ is the Gruneisen gamma, and pH and eH are expressed asfollows:

pH ¼ C20

1ρ0

� 1ρ

� ��1ρ0

� S1ρ0

� 1ρ

� �� �2, (12)

eH ¼ C20

1ρ0

� 1ρ

� �2�2

1ρ0

� S1ρ0

� 1ρ

� �� �2, (13)

C0 ¼ @p

@ρ

� �1=2

, (14)

S ¼ dUshock=dUparticle, (15)

Ushock ¼ C0 þ SUparticle, (16)

where C0 is the speed of sound, S is the linear Hugoniotslope, Ushock is the shock wave speed, and Uparticle is thematerial particle velocity. An isentropic Jones–Wilkins–Lee( JWL) EOS was used to calculate the isentropic pressure(pS) of the reacted state of the explosive, with v ¼ ρ0=ρ

pS ¼ A2e�R1v þ B2e

�R2v þ C2v�(ωþ1): (17)

The parameters in the above equation can be obtained with ametal cylinder expansion test or a thermochemical coderunning a cylinder test.11 The test measures the metal

TABLE III. Modeling constants for each explosive.

Parameter(unit)

RDX25

HMX66

HMX95 Pentolite

Reactant ρ0 (kg m−3) 1830 1900 1820 1560

C0 (m s−1) 2406 2467 2467 …

S 1.89 1.86 1.89 …

Γ 0.99 0.99 1.09 …

A1 (GPa) … … … 12.82B1 (GPa) … … … 0C1 (GPa) … … … 119.3

Product A2 (GPa) 628.6 652.2 458.0 481.7B2 (GPa) 4.80 4.10 8.30 8.93

R1 5.10 4.23 3.721 4.70R2 1.30 0.75 1.068 1.05ω 0.086 0.091 0.359 0.36

Chemicalkinetics

I (μs−1) 0.94 4.30 12.10 1.40a 4.0 4.0 4.0 4.0

G (μs−1 GPa−b) 0.105 0.236 0.538 0.829b 1.30 1.54 1.65 1.3

S!¼

� ρurr

w

srr � sθθ � ρu2rr

wþ η@srr@r

þ @szr@z

� �

szr � ρuruzr

wþ η@srz@r

þ @szz@z

� �

ursrr þ uzsrz � ur(ρE þ p)r

wþ η@(ursrr þ uzsrz)

@rþ @(urszr þ uzszz)

@z

� �

2666666666664

3777777777775

, (4)

215905-3 Baek, Kim, and Yoh J. Appl. Phys. 124, 215905 (2018)

displacement due to the expansion of detonation product byimpacting a copper-based explosive. Assuming that theexpansion degree of the metal is equal to that of the detona-tion product, the parameters are obtained by fitting proce-dures.11 However, reflected waves are generated from thecylinder wall, causing product recompression by wavessuperposition.12 Due to this high pressure effect, a non-isentropic JWL EOS rather than its isentropic form isrequired: the first law of thermodynamics for isentropicprocesses is given by

eS ¼ �pSdv, (18)

eS ¼ A2

R1e�R1v þ B2

R2e�R2v þ C2

ωvω, (19)

where ω is defined as follows:

ω ¼ vdp

de

v

: (20)

Then, the Taylor series of the isentropic EOS is developed asfollows:

p ¼ pS þ dp

de

v

(e� eS) ¼ pS þ ω

v(e� eS): (21)

By combining the above equations, we obtain the followingnon-isentropic JWL EOS:

preacted ¼ A2 1� ω

R1v

� �e�R1v þ B2 1� ω

R2v

� �e�R2v þ ωe

v,

(22)

where A2, B2, C2, R1, R2, and ω are JWL EOS parameters.Since there were no experimental data for the targetexplosives, we calibrated the parameters reported byFried et al.13

The pressure parameters for the unreacted and reactedstates are shown in Table III. The pressure was calculated asburned mass fraction as follows:

p ¼ (1� λ)punreacted þ λpreacted: (23)

The pressure of the gap material, PMMA, was calculatedwith the following Mie–Gruneisen EOS:14

pPMMA ¼ Γ0E

þ ρ0C20μ 1þ 1� Γ0

2

� �μ

� �=[1� (S0 � 1)μ]2,

(24)

where μ ¼ ρ=ρ0 � 1. The Johnson–Cook model was used tocalculate the yield stress (σY ) due to the gap material defor-mation as follows:

σY ¼ [A3 þ B3(εp)n](1þ C3 ln _εp) 1� T � T0

Tm � T0

� �, (25)

where εP is the effective plastic strain; _εP is the effectiveplastic rate; Tm is the melting point; T0 is the room tempera-ture; and A3, B3, C3, and n are modeling parameters for inertmaterials. Table IV shows the modeling constants forPMMA.

V. SIMULATION RESULTS

A. Unconfined rate stick test

For the unconfined rate stick simulation, there is a level-set boundary between void and explosive shown in Fig. 3:the length (Lx) was 100 mm for RDX 25 and HMX 66 and50 mm for HMX 95. Figure 4(a) shows the mesh resolutiontest results for RDX 25. The peak pressure of detonation atmesh resolution of 0.2 mm is confirmed to be the rightchoice for the simulation. Figure 4(b) compares the fullyresolved detonation structures for the three explosives. Thetwo HMX-based explosives have a high peak pressure and asharp structure after detonation, and a short reaction zonelength (<0.5 mm), while RDX 25 exhibits a low peak pres-sure and a longer reaction zone.

Table V shows that the calculated Chapman-Jouguetpressure, pcj, was almost equal to that reported by Cheetah.Table VI15 shows values for illustrating the effect of Al andAP addition to the explosives.

This oxidizer and fuel addition allows the increase oftotal energy and the reduction of detonation energy so thatthe deflagration effect as opposed to detonation lasts longer.Adding Al and AP decreases the peak pressure by decreasingthe detonation energy. However, Al and AP react after all ofthe basic explosive is consumed, increasing the total energy.Hence, RDX 25 has a longer tail than the other two explo-sives, as shown in Fig. 4(b). As regards HMX 66 with HMX 95,

TABLE IV. Modeling constants for PMMA.

Mechanical parameter (unit)ρ0 (kg m−3) 1182Young’s modulus (GPa) 0.42Shear modulus (GPa) 2.32

Thermal parameter (unit)Cp ( J kg

−1 K−1) 1466T0 (K) 300Tm (K) 330.3

Mie–Gruneisen equation of state (unit)C0 (m s−1) 2180S0 1.410Γ0 0.85

Jonson–Cook model (unit)A3 (GPa) 0.76B3 (GPa) 0.07C3 0.0m 1.0n 1.0

FIG. 3. Computational domain for the unconfined rate stick simulation.

215905-4 Baek, Kim, and Yoh J. Appl. Phys. 124, 215905 (2018)

the tail of the Al-containing explosive is longer, indicating thatthe addition of Al and AP effectively increased the impulseand reduced the peak pressure. Figure 5 shows the pressureevolution during detonation propagation of RDX 25. Due tothe subsequent burning of Al and AP, the pressure range ofRDX 25 is wider than that of the other two explosives. Thecombination of Al and AP increases the blast effect due to theabove mentioned combustion characteristics.

The detonation velocity declines with decreasing stickradius because the energy loss due to product expansionincreases as the radius becomes smaller.6 As a result, thepeak pressure decreases and the pressure gradient decreases.Figure 6 shows the variations of detonation velocity depend-ing on the size of the three explosives. The analytic solutioncorresponds to solving Eq. (26)

RD

R¼ �0:4

[1� (US=D)2]

�0:8

ln [1� (US=D)2]

US

D

� �2b�1

1� US

D

� �: (26)

Here, RD is the generalized radius, b is the pressure sen-sitivity, US is the detonation velocity, D is the detonationvelocity at infinite radius, and R is the radius. One can plotthe relation of the detonation velocity depending on theinverse radius obtained through the rate stick data. D is calcu-lated by extrapolating the data at inverse radius being zero.The optimum values of RD and b which minimize the differ-ence between Eq. (26) and experimental data are obtained bythe curve fitting procedure.

B. LSGT: Donor-gap pair

The LSGT was designed to determine the Go/No Go ofthe acceptor charge. Before calculating the complete train ofdonor–gap–acceptor, the pressure attenuation in the gap wasverified. Figure 7 compares the numerical results of theshock wave attenuation in the PMMA gap with the NavalOrdnance Laboratory (NOL) LSGT data.16

FIG. 4. Mesh resolution test results for RDX 25 with infinite radius (a) andcomparison of the resolved detonation structures of all the explosives ana-lyzed (b).

TABLE V. Calculated detonation properties of three heterogeneousexplosives.

Parameter (unit) RDX 25 HMX 66 HMX 95

Peak pressure (GPa) 19.3 43.0 47.5pcj (GPa) 16.0 30.0 33.0pcj (GPa, Cheetah) 16.6 29.1 34.1Reaction zone (mm) 5.0 0.4 0.2Mesh size (mm) 0.2 0.04 0.02

TABLE VI. Effects of Al and AP addition on RDX-based explosives.15

Explosive composition (%)Total energy

(kJ/kg)Detonation energy

(kJ/kg)

RDX 85, HTPB 15 5200 3708RDX 65, Al 20, HTPB 15 7917 3343RDX 20, AP 43, Al 25, HTPB 12 8505 1474

FIG. 5. RDX 25 rate stick pressure contour for radius 50, 30, and 17.5 mmcases (from top to bottom) at time 6.5, 11.5, and 16.5 μs (the length rangewas 0–100 mm).

215905-5 Baek, Kim, and Yoh J. Appl. Phys. 124, 215905 (2018)

With the configuration shown in Fig. 2, the pressureattenuation was calculated for a gap thickness of 60 mm. TheNOL and calculated data are in good agreement with thoseof shock pressure according to the measured thickness shownin the data. Because the impedance of the PMMA is smallerthan that of the donor, the pressure wave transmitted is

decreased. As the shock wave crosses the interface ofPMMA, the density of PMMA is increased due to a compres-sion. The relevant pressure attenuation is calculated throughEq. (24).

C. LSGT: Donor-gap-acceptor train

The numerical simulation of the donor–gap–acceptortrain was performed for all three explosives. The mesh sizewas 0.1 mm.4 The total length of the train is 150 mm, thegap and acceptor length for all explosives are specified inTable VII. After the shock wave, attenuated in the PMMAgap, is transmitted to the acceptor, the reaction hardly occursuntil the reaction progress of the acceptor reaches 0.01. In theGo case, the reaction progress reaches 0.01 at the ignitionstage, and the reaction continues to growth. In the No Gocase, the reaction progress asymptotically reaches the 0.01value. The reaction progress is maximum at the center of theinterface between gap and acceptor until the reaction reachesthe growth stage. When the reaction progress at this pointbecomes 0.01, a detonation occurs, where the energy at thispoint exceeds the threshold value and the reaction takesplace.

Figure 8 shows the propagation of the shock wave overtime for HMX 95. Since the acceptor impedance is largerthan the PMMA one, the transmitted shock wave is strongerin the acceptor in all cases. In the Go case, the incidentshock wave turns into a fully developed detonation wave asthe reaction progresses. This explosive turns into a fullydeveloped detonation quicker than the other explosives

FIG. 6. Size effect curves for (a) RDX 25, (b) HMX 66, and (c) HMX 95.

FIG. 7. Shock attenuation shown in PMMA.

TABLE VII. Gap thickness and acceptor length for gap test simulations.

Go/No Go RDX 25 HMX 66 HMX 95

PMMA gap (mm) Go 21.0 43.0 53.0No Go 22.0 44.0 54.0

Acceptor (mm) Go 79.0 57.0 47.0No Go 78.0 56.0 46.0

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because of the short reaction length required. The critical gapthickness which was experimentally obtained in Table II iswell predicted through the simulation results.

VI. CONCLUSIONS

The pressure-driven reaction model is proposed for theenhanced blast explosives that contain metallic fuel. In

particular, the characteristics of the reaction, subsequent tothe addition of aluminum and ammonium perchlorate in thepresence of HMX or RDX, were considered. The fuel-richcondition due to aluminum in excess together with theoxygen-rich condition due to ammonium perchlorate additionleads to an enhancement of the overall impulse of the explo-sion with extended duration of chemical reaction. Althoughshock initiation as measured by the gap test and size effectrelated to the rate stick tests were reproduced with a presentreactive burn model, a more advanced study is desired tounderstand the longer-time behavior of these complicatedmaterials.

ACKNOWLEDGMENTS

This study was carried out with the support of Agencyfor Defense Development and National Research Foundationof Korea (No. 2017R1A6A3A11031277) contracted throughIAAT at Seoul National University. The authors are gratefulto Dr. J. Park of ADD for providing the experimental data.

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FIG. 8. Time trace of the pressure for the (a) Go (53-mm gap) and (b) NoGo (54-mm gap) cases for HMX 95.

215905-7 Baek, Kim, and Yoh J. Appl. Phys. 124, 215905 (2018)